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Astronomy
&
Astrophysics
A&A 636, A91 (2020)
https://doi.org/10.1051/0004-6361/202037485
© ESO 2020
Time evolution of dust deposits in the Hapi region
of comet 67P/Churyumov-Gerasimenko
P. Cambianica1,3, M. Fulle2, G. Cremonese3, E. Simioni3, G. Naletto1,4,5, M. Massironi6,1, L. Penasa1,
A. Lucchetti3, M. Pajola3, I. Bertini7, D. Bodewits8, C. Ceccarelli9, F. Ferri1, S. Fornasier10, E. Frattin7, C. Güttler11,
P. J. Gutiérrez12, H. U. Keller13,14, E. Kührt14, M. Küppers15, F. La Forgia7, M. Lazzarin7, F. Marzari4, S. Mottola14,
H. Sierks11, I. Toth16, C. Tubiana11, and J.-B. Vincent14
(Affiliations can be found after the references)
Received 13 January 2020 / Accepted 13 March 2020
ABSTRACT
Aims. We provide a measurement of the seasonal evolution of the dust deposit erosion and accretion in the Hapi region of comet
67P/Churyumov-Gerasimenko with a vertical accuracy of 0.2–0.9 m.
Methods. We used OSIRIS Narrow Angle Camera images with a spatial scale of lower than 1.30 m px−1and developed a tool to
monitor the time evolution of 22 boulder heights with respect to the surrounding dust deposit. The tool is based on the measurement of
the shadow length projected by the boulder on the surrounding pebble deposit. Assuming the position of the boulders does not change
during the observational period, boulder height variations provide an indication of how the thickness of the surrounding dust layer
varies over time through erosion and accretion phenomena.
Results. We measured an erosion of the dust deposit of 1.7±0.2 m during the inbound orbit until 12 December, 2014. This value
nearly balances the fallout from the southern hemisphere during perihelion cometary activity. During the perihelion phase, the dust
deposit then increased by 1.4±0.8 m. This is interpreted as a direct measurement of the fallout thickness. By comparing the erosion
rate and dust volume loss rate at the Hapi region measured in the coma, the fallout represents ∼96%in volume of the ejecta. The
amount of the eroded pristine material from the southern hemisphere, together with its subsequent transport and fallout on the nucleus,
led us to discuss the pristine water ice abundance in comet 67P. We determine that the refractory-to-ice mass ratio ranges from 6 to 110
in the perihelion-eroded pristine nucleus, providing a pristine ice mass fraction of (8 ±7)%in mass.
Key words. comets: general – comets: individual: 67P/Churyumov-Gerasimenko – methods: data analysis – methods: numerical
1. Introduction
The European Space Agency’s Rosetta mission was designed
to orbit and land on the Jupiter-family comet 67P/Churyumov-
Gerasimenko (hereafter 67P). Rosetta arrived at its primary
target on 6 August, 2014. The probe was first guided into an
orbit around its target to perform a first analysis and find a suit-
able landing site for the lander module Philae. Rosetta revealed
that the nucleus of comet 67P consists of two lobes (Sierks
et al. 2015) connected by a narrow neck, with a stable spin
axis. The Optical, Spectroscopic, and Infrared Remote Imaging
System (OSIRIS, Keller et al. 2007) was designed to study the
nucleus and its dust and gas environment. The system consisted
of two cameras operating from near-ultraviolet to near-infrared
wavelengths. The Wide Angle Camera (WAC) imaged the dust
and the gas surrounding the nucleus with a spatial scale of
10.1 m px−1at 100 km from the surface. The comet nucleus and
its surface topography were investigated by the Narrow Angle
Camera (NAC) with a spatial scale of 1.86 m px−1at the same
distance. The OSIRIS observations revealed that the northern
regions, such as Ash, Ma’at, Seth, and Hapi (Thomas et al. 2015;
El-Maarry et al. 2015) are fully covered by dust. On the contrary,
equatorial regions, such as Anubis, Aket, and Bastet, look differ-
ent. In these regions, we observe consolidated and coarse terrain
instead of dust deposits (Keller et al. 2017). The nucleus rotates
with an obliquity of 52◦(Keller et al. 2007). Due to the inclina-
tion of the axis of rotation, the comet experiences strong seasonal
effects, resulting in significant differences in insolation between
the northern and southern hemispheres. This strong dichotomy
is reflected in the morphology of the two hemispheres. Southern
summer coincides with the perihelion passage, hence causing the
erosion in the southern hemisphere to be much stronger than in
the northern regions (Jorda et al. 2016;Keller et al. 2017). The
approach to perihelion causes a rise in the temperature of the
nucleus, sublimating the ices. Observations of the coma revealed
water to be the most abundant volatile (Gulkis et al. 2015). Keller
et al. (2017) calculated the erosion due to sublimation of water
ice to investigate the link between insolation, erosion, and water
content of the nucleus surface. The value was found to be four
times stronger on the southern hemisphere than on the north-
ern one. The strong insolation and the water ice content in the
south could erode the surface up to 20 m (Keller et al. 2017) at
perihelion. Instead, the northern hemisphere, particularly Hapi,
is characterized by a minimal amount of insolation, and there-
fore minimal erosion. These pieces of evidence confirmed that
the dichotomy in appearance between the two hemispheres is
linked to the dichotomy in erosion, and that the dust cover in
the northern regions could be the result of transport mechanisms
of particles from the southern hemisphere during the southern
summer (Keller et al. 2015).
In this study, we describe a tool we developed to quantify the
seasonal erosion and deposit and/or accretion in the Hapi region.
We started from this region to link the time evolution of dust
with the mass transfer mechanism and the erosion of the comet
Article published by EDP Sciences A91, page 1 of 13
A&A 636, A91 (2020)
surface. The tool is based on the monitoring of the time evolution
of boulder height, which is defined as the difference between the
top of the boulders and the surrounding pebble deposit surface.
This technique has led to measurements of the seasonal evolution
of the deposit erosion and/or accretion of the Hapi region with
a vertical accuracy of 0.2–0.9 m. The amount of erosion of the
southern hemisphere, the subsequent transport of material, and
then its fallout on the nucleus allow us to investigate the pristine
water ice abundance in comet 67P.
2. Mass transfer on 67P
The dichotomy in appearance between the two hemispheres of
comet 67P is linked to the dichotomy in erosion. The eroded
southern surface is subject to a strong insolation and water sub-
limation (Keller et al. 2015), contributing to the release of dust
particles of different sizes. OSIRIS detected both small dust
particles in the size range from 3×10−3up to 1 cm (Fulle
et al. 2016) and larger particles, named chunks. These objects
are defined as pieces of the nucleus of an average mass of 1 kg,
in the 10 to 20 cm range (Fulle et al. 2019). The dust particles
size–frequency distribution (SFD) allows us to link the ejection
mechanism with the water content of 67P. Fulle et al. (2019) cal-
culated the chunk volume ejected by 67P from 24 July, 2015, to
15 September, 2015. The lost volume is about 4×107m3, corre-
sponding to an eroded southern surface of about 10 km2(Keller
et al. 2015;Blum et al. 2017). This corresponds to an average
erosion thickness of about 4 m (Fulle et al. 2019). Assuming that
the southern erosion occurs because of the ejection of chunks
implies a total erosion in average steps of about 13 cm (Fulle
et al. 2019), involving a nucleus surface of 65 m2every second.
The erosion model developed by Keller et al. (2015) suggests that
the maximum water loss rate per unit area is 3×10−4kg m−2s−1.
This implies that from a nucleus surface of 65 m2, the water
loss rate is at most 0.02 kg s−1, which is a negligible mass frac-
tion of the corresponding chunk loss rate (Qv=8.3±2.1 m3
s−1;Fulle et al. 2019; namely the mass loss rate divided by the
bulk density). This result suggests that the chunk ejection from
the nucleus surface is dominated by perihelion erosion of the
southern hemisphere, but behaves independently of water ejec-
tion. As mentioned above, the dichotomy in appearance between
the two hemispheres is linked to the dichotomy in erosion. The
dust cover in the northern regions is the result of transport mech-
anisms of particles from the southern hemisphere during the
southern summer (Keller et al. 2015). Chunks ejected at perihe-
lion fall back over the whole nucleus, including Hapi. OSIRIS
observations of the nucleus reveal a surface characterized by
a varied surface granularity. Pebbles of ≈25 cm in size have
been observed in the Sais region (Pajola et al. 2017), suggest-
ing a deposit built up by chunks, and confirming the chunk
mass distribution in the 67P coma (Fulle et al. 2016;Ott et al.
2017). The distribution of pebbles in different regions, includ-
ing Hapi, can be explained with the dust fallout mechanism,
which causes chunks ejected during perihelion to fall back over
the whole nucleus. As the outbound equinox approaches, the
southern erosion decreases, and the outgassing in the northern
hemisphere self-cleans the fallout, removing the dust and leav-
ing chunks, because the nucleus outgassing is too low to lift these
objects.
The refractory-to-ice mass ratio. Water content and deliv-
ery to the terrestrial planets is still a subject of debate. Water is
present in different bodies of the Solar System, even in the outer
asteroid belt and beyond in the form of ices. Primitive meteorites
such as CI-chondrites are believed to come from C-type aster-
oids that dominated the outer part of the asteroid belt (Burbine
et al. 2002), and can have ∼5–20%water by mass (O’Brien et al.
2018). Growth processes of carbonaceous CI-chondrites, charac-
terized by a chemical composition mostly resembling the solar
photosphere, allow water to be trapped in their silicates at a
molecular scale (Garenne et al. 2014). Ordinary chondrites are
linked to S-type asteroids, which are present in the inner aster-
oid belts, and contain a different amount of water. As regards
comets, they are formed beyond Neptune and their water was
incorporated in the form of ices embedded in the refractory
matrix of their nuclei (Blum et al. 2017). The radial distribution
of water and ices is recorded in the refractory-to-ice mass ratio in
comets (Fulle et al. 2019). This ratio is a fundamental parameter
which constrains the origin of comets and Kuiper Belt objects
(KBOs). Quantifying the difference in water content between
comets and other bodies allows us to distinguish between dif-
ferent formation processes, providing knowledge on the origin
of the Solar System.
As mentioned above, chunks ejected at perihelion fall back
over the whole nucleus, including Hapi. As the outbound
equinox approaches, the outgassing from the southern hemi-
sphere decreases due to seasonal changes, increasing the out-
gassing in the northern hemisphere where fallout occurred
around perihelion (Fulle et al. 2019). Outbound, the self-cleaning
in the Hapi region is negligible, and possible only from 2.5 to
4 au outbound (Fulle et al. 2019). This implies that Hapi ejects
sub-centimetre dust only (Rotundi et al. 2015), acting as a chunk
deposit with a thickness of metres. This can be explained as
follows. Chunks ejected at perihelion have a refractory-to-ice
mass ratio larger than inside the nucleus, and have an upper
exposed dehydrated crust, the thickness of which increases as the
refractory-to-ice mass ratio increases (Fulle et al. 2019). Fresh
ice on Hapi is exposed to sunlight by water ice migration to the
surface (De Sanctis et al. 2015) and by the removal of chunks of
dehydrated crust. This causes outgassing coming from the inte-
rior of the chunks (Fulle et al. 2019), preventing any outgassing
from below the surface.
Keller et al. (2017) calculated the water production of the
nucleus along its orbit. These latter authors found that the pro-
duction rates of the northern regions follow the insolation trend,
and are controlled by the peculiar shape of the nucleus and the
inclination of the spin axis. Hapi represents the conjunction point
between the two lobes. This cavity reached insolation for short
intervals of a cometary day because of the shading by the lobes
(Pajola et al. 2019). This should mean that this region cannot be
as active as other regions located in the south. However, Hapi
appears to be the most active area during northern summer as
a consequence of its water content and morphology. Because of
the morphology of this region, the absorbed energy is not suffi-
cient to produce strong outbursts, as observed elsewhere on the
nucleus, but allows a modest continuous activity also far from
perihelion. The activity is due to a thinner desiccated dust layer
which accumulates after perihelion because of the fall out, and is
eroded by ice sublimation when approaching the sun again after
aphelion (Keller et al. 2017). In this context, the seasons of Hapi
are fundamental to link (Fulle et al. 2019) its processed ice abun-
dance to the pristine ice content of the metres-thick layers eroded
every perihelion from the southern nucleus hemisphere.
3. Data and method
The Hapi region is located in the northern hemisphere (Thomas
et al. 2015), between the two lobes of comet 67P. It has been
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P. Cambianica et al.: Time evolution of dust in the Hapi region of comet 67P/Churyumov-Gerasimenko
Table 1. NAC-OSIRIS images used in this work.
NAC-OSIRIS image (m px−1)
NAC_2014-08-21T16.42.56.549Z_ID30_1397549300_F22 1.26
NAC_2014-08-21T19.42.54.558Z_ID30_1397549900_F22 1.25
NAC_2014-08-21T20.42.54.581Z_ID30_1397549100_F22 1.25
NAC_2014-08-22T08.42.54.550Z_ID30_1397549000_F22 1.26
NAC_2014-08-28T20.42.53.590Z_ID30_1397549900_F22 1.01
NAC_2014-08-29T14.42.55.551Z_ID30_1397549700_F22 1.02
NAC_2014-08-29T20.42.53.538Z_ID30_1397549900_F22 1.02
NAC_2014-08-29T21.42.53.565Z_ID30_1397549100_F22 0.99
NAC_2014-08-29T23.12.53.524Z_ID30_1397549500_F22 1.01
NAC_2014-08-30T02.42.53.544Z_ID30_1397549800_F22 1.04
NAC_2014-08-30T03.42.53.546Z_ID30_1397549000_F22 1.05
NAC_2014-08-31T15.42.53.546Z_ID30_1397549000_F22 1.24
NAC_2014-09-01T16.42.53.551Z_ID30_1397549400_F22 0.97
NAC_2014-09-10T11.54.24.601Z_ID30_1397549000_F24 0.55
NAC_2014-09-22T21.09.48.386Z_ID30_1397549000_F16 0.54
NAC_2014-12-10T06.29.11.447Z_ID30_1397549002_F24 0.37
NAC_2016-06-19T11.09.40.836Z_ID30_1397549000_F41 0.56
NAC_2016-06-19T15.30.03.468Z_ID30_1397549004_F16 0.54
NAC_2016-09-30T03.37.09.738Z_ID30_1397549200_F22 0.26
Notes. The first three letters indicate the instrument used to acquire
the image; the following digits are the time (in UTC) of imaging (year-
month-day, then hour-minute-seconds) as reported in the file name (this
time is not corrected for S/C drift and leap seconds); the last two num-
bers correspond to the used filter identifier. The spatial scale (m px−1) is
shown.
classified as a deposit of debris (Thomas et al. 2015), and
is characterized by a distribution of boulders and/or outcrops
(Cambianica et al. 2019) scattered all over the debris plain. Hapi
is also dominated by smooth terrain (El-Maarry et al. 2015) and
dune fields. Due to the presence of boulders and outcrops of tens
of metres in size, El-Maarry et al. (2015) suggested a dust deposit
thickness of several metres. The neck region corresponds to the
gravitational minimum of the nucleus (Keller et al. 2017) and is
therefore considered as the preferred location for the accumula-
tion of the back-falling material (Keller et al. 2017). To measure
the erosion and deposition of dust in this region, we monitored
changes in the height of boulders, assuming that these objects are
not involved in erosion processes, and that it is the surrounding
terrain that gains height or is eroded.
3.1. Data selection
For the analysis of dust erosion and deposit on the Hapi region
we used 19 OSIRIS NAC images (see Table 1for image IDs)
and the photogrammetric SHAP8 V.2.1 (issued by Gaskell and
Jorda in March 2018) comet shape model, which represents
an advanced model based on a data set of 20679 OSIRIS-
NAC images and 6072 OSIRIS-WAC images acquired between
11 July, 2014, and 30 September, 2016. The shape model can
therefore be considered as a mean model of the surface, in
which the evolution of the surface morphology cannot be appre-
ciated. We divided the data set into two groups. The first set
of 16 NAC images was acquired from 21 August, 2014, to 10
December, 2014, which is before the comet inbound equinox.
The spatial scale ranges from 1.26 to 0.37 m px−1. The sec-
ond set of three NAC images was acquired from 19 June, 2016,
to 30 September, 2016 (spatial scale of 0.56, 0.54, and 0.26
m px−1, respectively) after the outbound equinox. We developed
Table 2. ID, latitude, and longitude of the analyzed boulders.
ID boulder Latitude Longitude
(◦) (◦)
1 27.69 18.20
2 30.76 22.61
3 30.25 30.35
4 33.82 31.72
5 33.39 27.18
6 36.58 20.36
7 38.93 22.81
8 40.52 25.49
9 36.86 9.64
10 36.09 7.92
11 39.50 12.15
12 39.71 7.98
13 50.93 354.56
14 55.09 345.15
15 49.93 0.03
16 56.05 2.95
17 59.19 6.85
18 47.03 357.43
19 51.33 0.60
20 47.92 4.99
21 44.89 5.62
22 31.06 25.07
a MATLAB (MATLAB 2010) tool to monitor the time evolu-
tion of boulder heights from 21 August, 2014, up to the end of
the mission. The height is defined as the difference between the
top of the boulders and the surrounding pebble deposit surfaces.
The tool is based on the measurement of the shadow length
projected by the boulder on the surrounding pebbles deposit.
This technique relies on the geometric Spice Kernel data (Acton
1996) and requires high-resolution images (at least 1.30 m px−1).
High-resolution NAC images provided global views of the Hapi
region, allowing us to analyze as many boulders as possible.
According to the illumination and visibility conditions, we mea-
sured the height of 22 boulders. The locations of the boulders is
shown in Fig. 1. The figure reports the corresponding ID for each
boulder (see Table 2for the ID of the boulders and their latitudes
and longitudes).
3.2. Surface plane definition and image alignment
To measure the height Hof a boulder, we have to consider the
projection of the OSIRIS NAC image on the 3D shape model
of the comet. To obtain the correct projection, we defined a set
of uniquely identified tie points both on the shape model and
on the images. From the correspondence between these points,
we derived the proper homography transformation for each pro-
jective system. This method allows us to refine the instrument
attitude minimizing the residuals of the 3D points projected on
the images. As a result, we can associate a corresponding 3D
point on the surface photogrammetric model to each pixel of the
images. Once the misalignment between the two is corrected,
and the proper boulder is identified, it is possible to define an
average surface plane Σaround the boulder in which the boul-
der shadow is projected (see Fig. 2). The definition of an average
surface plane is fundamental to avoid the local granularity of
the mesh and to smooth possible surface irregularities, since
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A&A 636, A91 (2020)
Fig. 1. Zoom of the image from 21 August, 2014, (NAC_2014-
08-21T16.42.56.549Z_ID30_1397549300_F22). The figure shows the
corresponding ID for each boulder reported in Table 2.
Fig. 2. Schematic representation of the adopted geometry and of the
parameters used for determining the boulder height. Σis the average
surface plane, Πis the plane containing the normal nto Σand the illu-
mination vector, iis the incidence angle, Qrefers to the peak of the
shadow, which is defined by the highest point of the boulder P, and Lis
the length of the shadow. Finally, His the height of the boulder.
the topography of Hapi is nonhomogeneous. The definition of
the average surface is defined by a grid of 3D points around
the contour of the boulder and a suitable interpolation of these
points. The resulting point cloud is then decomposed in eigen-
vectors. The eigenvector associated to the minimum eigenvalue
represents the normal to the surface. Other parameters to be
defined are the incidence angle iof the solar direction with
respect to the normal to the plane Σ, and the length Lof the boul-
der shadow. These three elements completely define the adopted
geometry for determining the boulder height.
3.3. Boulder profile reconstruction and height calculation
As mentioned before, the 3D model cannot be used to directly
measure the height of a given because it does not take into
Fig. 3. Plot a: NAC view of the Hapi region (0.37 m px−1); this image
was acquired in 2014. Plot b: close-up of a boulder and of its shadow.
The green line represents the projection of the Sun illumination direc-
tion. Plot c: boulder section (we note the different scales on the plot
axes deforming the boulder shape). The y-axis is oriented as the nor-
mal to the average plane around the peak of the shadow. The x-axis is
obtained by projecting the green line in plot b on this average plane; the
x-axis origin coincides with the peak of the shadow. We note that by
comparing plots b and c, the shadow lengths appear different because
of projection effects.
account variations in the surface morphology. For this reason,
we adopted a technique based on the assumption that the surface
normal to Σis considered to be locally time-invariant and based
on the definition of the illumination vector, which uniquely iden-
tifies the position of the peak of the shadow Q(see Fig. 2) on
the average surface Σ, and therefore on the 3D model. The peak
is defined as the point of the shadow contour with the longest
extension along the illumination direction, and originates from
the highest point of the boulder P. Following this, it is neces-
sary to define a plane Πperpendicular to Σwhich contains the
direction of the illumination direction, and passes through the
point Q. This plane cuts the boulder along the direction of
the solar illumination and passes through its highest point P. The
bi-dimensional boulder profile obtained by sectioning the comet
shape model with the plane Πfinally allows us to determine the
position of the peak P, which is the highest boulder point tangent
to the illumination direction. The length Lof the shadow on the
Σplane can then be defined as the distance between the Qpoint
and the projection of Pon Σ. Finally, the boulder height Hcan
be calculated as follows:
H=L·tan π
2−i,(1)
where Lis the length of the shadow and iis the incidence angle.
In Fig. 3an example of the height measurement is shown. After
the identification of the proper boulder and definition of the
average surface plane, the Sun illumination direction is calcu-
lated (see the green line in Fig. 3, plot b). After the manual
selection of the peak of the shadow (which corresponds to the
origin of the x-axis in plot c of Fig. 3) and the projection of
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P. Cambianica et al.: Time evolution of dust in the Hapi region of comet 67P/Churyumov-Gerasimenko
Fig. 4. Gravitational slopes of the 67P nucleus surface. The centrifu-
gal force is included. The values are restricted to the 0◦–60◦ranges
to emphasize the slopes below the repose angle of loose materials
(Groussin et al. 2015). The green ellipse defines the surface of 0.2 km2
encircling all the boulders considered in this work.
the illumination vector on the average plane, the height of the
boulder is calculated.
3.4. Gravitational slope
To confirm that our measurement has not been performed on
a deposit the thickness of which is altered by local gravita-
tional instability processes, for example landslides and granular
flows, or on a local point of fallout accumulation on the comet
surface, we investigated the surface gravitational slope. The
gravitational slope is defined as the angle between the local
surface normal and the vector opposite to the estimated accel-
eration field (Penasa et al. 2017). As shown in Fig. 4, the whole
Hapi region has gravitational slopes ranging between 0◦and 20◦,
lower than the angle of repose of loose granular materials on 67P
of (45 ±5)◦(Groussin et al. 2015). This is consistent with the
assumption that Hapi deposits are the result of a homogeneous
deposition driven by fallout.
3.5. Method validation
To validate the method, we performed a comparison test.
El-Maarry et al. (2017) measured the height of a boulder located
in the Imhotep region (see Fig. 5for the location of the region
and the considered boulder) finding a value of 3.9 +0.1/−0.2 m in
height. We applied our method to the same boulder and we found
4.08 ±0.35 m, which is a value consistent with the determination
of El-Maarry et al. (2017). The two methods being completely
independent, this check confirmed the reliability of our method.
4. Results
According to Eq. (1), we calculated the incidence angle (i) and
the length of the shadow (L) to measure the height of 22 boul-
ders. A summary of the boulder height measurements is reported
in Table A.1. We provide the corresponding universal time coor-
dinated (UTC), the calculated incidence (i) and emission (e)
angles, the measured length of the shadow (L), and the height
(H) of boulders with the associated average error bar (δH). As
shown in Eq. (1), the height calculation does not depend on the
emission angle, which is defined as the angle of camera bore-
sight relative to the surface normal. However, we report both
Fig. 5. OSIRIS-NAC image taken on 25 December, 2016 (NAC_2016-
05-25T15.32.54.769Z_1397549100_F22). The white circle indicates the
analyzed boulder. Bottom right panel: location of the Imhotep region on
the comet nucleus.
the emission and incidence angle values to show the statistical
variability of the images used. To mediate the error bars, we
used OSIRIS NAC high-resolution images with the best visi-
bility conditions to compare as many heights as possible. We
measured 22 boulders, but some measurements have not been
included because of their large uncertainty due to the adverse
illumination or visibility conditions. The reported error bars have
been estimated propagating the individual errors associated to
the selection of the pixel identified as the shadow peak, and the
calculation of the incidence angle. The accuracy of the manual
selection of the pixel depends on the ability of the operator to
select the proper pixel. The accuracy of the incidence angle cal-
culation strongly depends on the definition of the normal to the
Σplane. This is associated to the standard deviation of the dis-
tance between the surface points around the boulder and the Σ
plane. To estimate the accuracy of the Σdefinition, and therefore
the accuracy of the incidence angle calculation, we investigated
the impact of the granularity on the incidence angle. We per-
formed a Monte-Carlo simulation which consists in defining a
set of surfaces with different vertical standard deviations. These
values represent the granularity of the surface. The estimation
of the normal and the calculation of the incidence angle are per-
formed by calculating the previously defined eigenvectors (see
Sect. 3.2). Figure 6shows the results of the Monte-Carlo sim-
ulation. The incidence angle being related to the definition of
the above-mentioned normal, the derived standard deviations for
the measured surfaces range between 0.02 and 0.1 m. As seen in
Fig. 6, in this range the maximum error on the incidence angle
value is lower than 0.5◦. After measuring the height of each boul-
der, we calculated the corresponding maximum and minimum
values considering the associated errors (see Table A.1). These
values have been obtained as follows:
Hmin/max =[L∓δp(POG∓δl)]tanπ
2−(i±δi),(2)
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A&A 636, A91 (2020)
Fig. 6. Incidence angle error as a function of the surface standard
deviation, which refers to the surface granularity.
where Lis the calculated length of the shadow, δpis the error
due to the manual selection of the peak of the shadow, the POG is
the pixel on ground (target–spacecraft distance multiplied by the
pitch size and divided by the focal length), δlis an error related
to the uncertainty of the Digital Terrain Model (δl=δh·tan(e),
where δhis the average uncertainty of the location of the DTM
with respect to the zero level of the image, and eis the emission
angle), iis the incidence angle, and the error on the incidence
angle, δi, is estimated to be equal to 0.5◦(see Fig. 6).
To better analyze the data, the images were divided into
subsets as follows:
– Subset 1: 21–22 August, 2014;
– Subset 2: 28 August, 2014–1 September, 2014;
– Subset 3: 10–22 September, 2014;
– Subset 4: 10 December, 2014;
– Subset 5: 19 June, 2016;
– Subset 6: 30 September, 2016.
This allowed us to identify differences in height (∆H∗) between
a generic image and the height measured on 21 August, 2014.
Having used 19 images, per subset there is more than one image
for which the boulder heights can be measured. Therefore, we
calculated the weighted average height of each boulder hHi. The
associated error δ(hHi)is calculated as follows:
δ(hHi)=1
pΣ(1/δH)2,(3)
where δHis the largest absolute value difference between the
measured height and HMin/Max.
The reported ∆Hvalues are the differences between the
<H>of two subsets, ∆H=<Hi>−<Hj>. The associated error
is finally calculated as:
δ∆H=qδ(<Hi>)2+δ(<Hj>)2.(4)
In Tables 3and 4, the time evolution of the weighted average
height of each boulder and the time evolution of the boulder
height difference ∆Hare shown. The graphical representation
of these results is shown in Fig. A.1.
The formula we used to calculate the weighted mean
∆Hweighted of the data sets ∆Hiwith corresponding error bars
δ∆Hishown in Table 4is:
∆Hweighted =Pn
i=1(wi·∆Hi)
Pn
i=1wi
,(5)
where wi=1/(δ∆Hi)2. The standard error of the weighted mean
is given by
δ∆Hweighted =
v
tn
X
i=1
wi
−1
.(6)
5. Discussion
We present observations by the Rosetta mission of comet 67P
which have allowed us to quantify the seasonal evolution and
deposit and/or accretion in the Hapi region. Figure 7shows the
time evolution of the heights of boulders on the surface of the
comet during the observations. Here the difference ∆H∗between
the height measurement of a generic image and the height mea-
sured on 21 August, 2014, is shown as a function of time. We find
a systematic increase of ∆Hof about 2 m over 2014 and then a
decrease by a similar amount between the equinoxes followed by
a plateau up to the end of the observations. The assumption here
is that any height variation is not due to boulder intrinsic changes
but to erosion or accretion of the surrounding pebbles and dust
deposits; due to the dominant cross-section of the fallout chunks
(from 80 up to 350 cm2;Fulle et al. 2019), only a minimal frac-
tion of the fallout remains settled on the top of the boulders.
Furthermore, following the method developed by Cambianica
et al. (2019), we analyzed the location and the morphology of
these boulders and outcrops, and no variation in morphology
or position of the boulders was seen during the mission. The
erosion of the southern hemisphere, the subsequent transport of
material, and then its fallout on the nucleus (Fulle et al. 2019;
Keller et al. 2017) are responsible for the time evolution of the
height of the boulders, which is linked to the likely source of
the deposit surrounding them. This mainly happens at the peri-
helion phase (Fulle et al. 2019;Keller et al. 2017), as evidenced
by the similarity between the size distributions of large particles
suspended in the coma (Fulle et al. 2016;Ott et al. 2017) and
the cobbles in Sais and Agilkia regions (Pajola et al. 2017). The
measured decrease of the boulder heights at the perihelion phase
from 2014 to 2016, δ∆H2014−2016 =−1.4 ±0.4 m, is therefore
interpreted as a direct measurement of the fallout thickness. This
value matches the predicted (Fulle et al. 2019) fallout thickness
of 1.8 ±0.7 m, revealing a consistency between the perihelion
erosion and the total loss of nucleus mass per orbit (Pätzold et al.
2018). The height difference between the boulders and the debris
field steadily increases during the inbound orbit, indicating an
ongoing erosion of the deposits in the Hapi region before the
comet reached its spring equinox. As shown in Fig. 7, between
June and September, 2016, ∆Hvariations are lower than their
error bars, consistent with negligible fallout and erosion after
the outbound equinox. This is consistent with the process that
has been suggested to be the main driver of the fallout (Fulle
et al. 2019;Bertini et al. 2018), namely the expelled chunks in
bound orbits are slowed by friction with the coma gas and finally
collapse onto the nucleus. After the outbound equinox, the coma
of 67P is too tenuous to further affect the chunk motion.
5.1. Erosion rate
The negligible erosion of the Hapi region from June to Septem-
ber, 2016, also suggests that Hapi maintains all its ice during
the outbound orbit, up to the next inbound activity (Fulle et al.
2019;Keller et al. 2017). Any possible ice regression without
dust ejection would soon build up an insulating crust of thickness
A91, page 6 of 13
P. Cambianica et al.: Time evolution of dust in the Hapi region of comet 67P/Churyumov-Gerasimenko
Table 3. Time evolution of the weighted average height of each boulder.
S1 S2 S3 S4 S5 S6
Boulder hHi ± δhHi hHi ± δhHi hHi ± δhHi hHi ± δhHi hHi ± δhHi hHi ± δhHi
(m) (m) (m) (m) (m) (m)
1 8.4 ±0.5 9.1 ±0.4 9.8 ±0.4 8.2 ±1.5
2 10.5 ±0.5 11.1 ±0.4 11.6 ±0.4 12.1 ±1.5 11.1 ±1.3
3 6 ±0.7 6.7 ±0.3 7.2 ±0.3 7.7 ±1.4 6.3 ±1.3
4 13.2 ±0.3 13.9 ±0.4 14.3 ±0.7 14.8 ±1.5 13.5 ±1.2
5 10.6 ±0.4 11.3 ±0.3 11.8 ±0.6 12.4 ±1.3 11.4 ±1.2
6 27.9 ±0.3 28.6 ±0.2 29.2 ±0.5 27.7 ±0.9
7 15.6 ±0.6 16.2 ±0.4 16.8 ±0.5 17.3 ±1.4 15.9 ±1.3
8 5.8 ±0.2 6.3 ±0.3 6.8 ±0.2 5.8 ±1.7 5.7 ±1.2
9 11.3 ±0.8 11.9 ±0.6
10 4.1 ±0.4 4.7 ±0.7 3.3 ±2.7
11 29.8 ±0.3 30.5 ±0.3 31.1 ±0.8 31.5 ±1.0
12 17.2 ±0.4 18.0 ±0.3 18.5 ±1.0
13 16.9 ±0.4 17.7 ±0.3 18.1 ±1.1 16.9 ±1.0
14 17.5 ±0.5 18.2 ±0.3 18.7 ±1.1 19.2 ±0.9 17.8 ±1.3 17.4 ±1.2
15 21.7 ±0.3 22.3 ±1.0 20.1 ±1.1
16 17.4 ±0.4 18.1 ±0.3 18.6 ±1.0 19.1 ±1.3 17.6 ±0.8 17.7 ±1.1
17 10.5 ±0.7 11.2 ±0.4 11.8 ±1.2 12.3 ±0.9 10.6 ±1.2 10.6 ±1.5
18 4.2 ±0.8 5.1 ±0.4 5.6±1.9 6.1 ±2.1 4.5 ±2.9 4.4 ±1.8
19 10.4 ±0.3 11.1 ±1.5 11.6 ±1.4 9.7 ±1.7 9.7 ±1.7
20 5.4 ±0.7 6.2 ±0.7
21 8.1 ±0.7 8.8 ±0.6 9.6 ±0.8 8 ±1.7
22 3.4 ±0.4 4.1 ±0.5
Notes. Each subset (S) contains the weighted average height (hHi) of each boulder and the associated error (δhHi).
Table 4. Time evolution of the boulder height difference ∆H.
S2–S1 S3–S2 S4–S3 S5–S4 S6–S5
Boulder ∆H±δ∆H∆H±δ∆H∆H±δ∆H∆H±δ∆H∆H±δ∆H
(m) (m) (m) (m) (m)
1 0.7 ±0.6 0.6 ±0.6
2 0.6 ±0.7 0.5 ±0.6 0.5 ±1.5 −1.1 ±2.0
3 0.7 ±0.7 0.5 ±0.4 0.5 ±1.5 −1.4 ±2.0
4 0.7 ±0.5 0.4 ±0.8 0.5 ±1.6 −1.3 ±1.9
5 0.6 ±0.5 0.6 ±0.8 0.5 ±1.4 −0.9 ±1.7
6 0.7 ±0.4 0.6 ±0.6
7 0.7 ±0.8 0.5 ±0.7 0.5 ±1.5 −1.4 ±1.9
8 0.5 ±0.3 0.5 ±0.4 −1.0 ±1.7 −0.2 ±2.2
9 0.6 ±1.0
10 0.4 ±0.8
11 0.7 ±0.4 0.6 ±0.8 0.5 ±1.2
12 0.7 ±0.6 0.5 ±1.1
13 0.7 ±0.5 0.5 ±1.2
14 0.8 ±0.5 0.5 ±1.1 0.5 ±1.4 −1.4 ±1.6 −0.4 ±1.8
15 0.6 ±1.0
16 0.8 ±0.5 0.5 ±1.1 0.5 ±1.7 −1.6 ±1.5 0.2 ±1.4
17 0.7 ±0.8 0.6 ±1.3 0.5 ±1.5 −1.6 ±1.5 0.1 ±1.9
18 0.9 ±0.9 0.5 ±2.0
19 ±0.6 ±1.5 0.5 ±2.0 −1.8 ±1.9 0.2 ±2.1
20 0.8 ±1.0
21 0.7 ±0.9
22 0.6 ±0.6
Weighted average 0.7 ±0.2 0.5 ±0.2 0.5 ±0.3 −1.3 ±0.6 −0.1 ±0.9
Notes. Each time step contains information related to 22 boulders. The height differences for each boulder and the weighted averages with the
associated error bars are reported.
A91, page 7 of 13
A&A 636, A91 (2020)
Fig. 7. Time evolution of the boulder height differences ∆H∗(as defined in text). Each time step contains information related to 22 boulders
and the values correspond to the weighted average. The y-axis reports the average height measurements referring to the subsets described in
Sect. 4. Subset 1 refers to 21–22 August 2014. According to the illumination and visibility conditions, the time interval between Subset 1 and the
perihelion is about 4 months. The time interval between the perihelion and Subset 6 is about one year. Erosion during the inbound orbit until
December, 2014, nearly balances the fallout from the southern hemisphere during perihelion cometary activity. The dotted red line indicates the
perihelion.
of a few centimetres at most (sufficient to dump any further ice
sublimation), thinner than the chunk size. Knowing the amount
of eroded material (∆H), we calculated the average erosion rates.
This value can be calculated as follows:
RateErosion =∆H×A
δt,(7)
where Ais the area of the considered elliptical surface encir-
cling all boulders and δtis the time interval under consideration.
The average erosion rate decreases from 0.15 ±0.07 m3s−1
in August, 2014, to 0.06 ±0.03 m3/s in September, 2014, and
to 0.012 ±0.010 m3s−1in October-December, 2014. Since the
adopted surface of 0.2 km2is only 10%of the surface of the Hapi
region, and there is no reason for the deposits in this latter region
to only be eroded around the boulders, it is reasonable to assume
that these are just lower limit values of the global erosion rates.
5.2. Dust fallout
The illumination and temperature of the Hapi region did not
change significantly from August to October 2014 (Tosi et al.
2019), which is when we measure surface erosion of the order of
metres. Therefore, a certain physical evolution of the terrain must
be assumed to explain this phenomenon, and the most reasonable
mechanism is the fallout self-cleaning (Fulle et al. 2019;Pajola
et al. 2017). Chunks falling onto the nucleus surface are rich in
ice as they have been freshly expelled from the active southern
hemisphere, and, if irradiated, they outgas and self-clean. In the
Hapi region, this outgassing and self-cleaning activity is absent
during the fallout season, when Hapi is in winter time, and is
almost negligible after outbound equinox because Hapi is in a
rather shadowed location. However, outgassing and self-cleaning
become more intense before reaching inbound equinox, which
is exactly when we observe the erosion phenomenon. Subse-
quently, as the comet gets closer to the Sun and Hapi approaches
its winter again, outgassing decreases in the Hapi region, is no
longer able to remove the chunk dehydrated crust, and the ero-
sion rate decreases and the process stops. At the same time, the
activity of the southern hemisphere increases again, as do the
total gas- and dust-loss rates (Fougere et al. 2016), and the cycle
is repeated.
It is also possible to directly estimate the fallout amount on
the comet nucleus associated to the activity of the neck region in
August 2014. In fact, by comparing the erosion rate in the Hapi
region in that month (0.15 ±0.07 m3s−1) with the dust volume
loss rate measured in the coma in the same period (0.006 m3s−1;
Migliorini et al. 2016), we can see that the former is 25 times
larger than the latter. Since Hapi was contributing for the most
part to the comet outgassing in August 2014, we can see that
the volume loss rate measured in the coma is only 4% of the
total erosion. This implies that the remaining 96%in volume of
material eroded from Hapi is falling again on the comet nucleus
surface. Fulle et al. (2018) estimated that the fallout at perihelion
is about 80%of the total southern eroded volume. The larger
fallout value measured here is probably due to the peculiar struc-
ture of the neck, which is a region surrounded by steep walls:
this makes it more difficult for the particles to escape the comet
because of the high probability of collision with the walls, and
increases the fallout percentage (Shi et al. 2018).
5.3. Water ice fraction in the Hapi region
As mentioned before, the measurement of the deposit erosion
and/or accretion in the Hapi region allows us to investigate the
A91, page 8 of 13
P. Cambianica et al.: Time evolution of dust in the Hapi region of comet 67P/Churyumov-Gerasimenko
pristine water ice abundance in comet 67P. The power index
of the differential dust size distribution at dust sizes >1 mm
has been calculated to be equal to −4 (Rotundi et al. 2015),
which, compared to that of the fallout from Hapi, constrains
its composition in particles smaller than 1 cm, meaning that its
bulk density is ρb=800+500
−100 kg m−3measured in sub-millimetre
particles (Fulle et al. 2017).
The bulk density allows us to calculate the dust mass loss
rate Qmin August, 2014, from the considered area A, as follows:
Qm=ρb×Rateerosion.(8)
The dust mass loss rate becomes 120+160
−60 kg/s. The ratio
between the erosion rate and the corresponding water vapour loss
rate of 1.2 kgs−1(Gulkis et al. 2015) provides Hapi’s dust-to-
water mass ratio (Rotundi et al. 2015) at the erosion of 100+140
−50 .
Coming from the crust of the chunks in the deposit (Fulle et al.
2019), the dust ejected by Hapi is dry (Fulle et al. 2018). This
is supported by the match between the water loss rates provided
by local (ROSINA) and remote (MIRO) observations (Marshall
et al. 2017) in August, 2014, which are <1% in mass of Hapi’s
measured erosion rate. This fact allows us to infer the ice mass
fraction of the Hapi region from the measured dust-to-water
ratio. The inverse of the dust-to-water ratio provides Hapi’s water
ice fraction of (1.2±0.8)% in mass. The lower limit of the dust-
to-water ratio corresponds to a water ice fraction of 2% in mass.
Since the dust ejected from the surface of the Hapi region was
probably greater than 0.2 km2in total volume, this value can be
considered as an upper limit (a larger area means an increase
of the dust volume). The fallout from Hapi is inert, but Hapi’s
erosion of 1.7±0.2 m during the inbound orbit is statistically
diluted by a factor of about 250 (namely, the total nucleus sur-
face divided by 0.2 km2), providing an average dry fallout of
<1 cm thick over the whole nucleus. This layer is negligibly thin
with respect to the total southern erosion of at least 4 m (Fulle
et al. 2019), with about 97% in volume of the total ejected mate-
rial in chunks of sizes >1 cm according to the perihelion dust
size distribution (Fulle et al. 2016).
6. Conclusions
In this study, we measured the seasonal evolution of the deposit
erosion and/or accretion in the Hapi region of the comet 67P with
a vertical accuracy of 0.2–0.9 m, quantifying the mass transfer
mechanism from the southern to the northern hemisphere of the
comet. To this aim, we developed a tool based on the monitor-
ing of the time evolution of 22 boulders located in the neck of
the comet, a region named Hapi. This region is located in the
northern hemisphere, and represents an ideal region for apply-
ing the method. This region is considered to be the preferred
location for the accumulation of material coming from the south-
ern hemisphere (Keller et al. 2017). We find that erosion during
the inbound orbit until December, 2014, nearly balances the fall-
out from the southern hemisphere during perihelion cometary
activity. A comparison between the eroded material and the dust
volume loss rate measured in the coma provided the amount of
fall back material due to the morphology of the Hapi region. The
fallout represents 96%of the eroded volume and is consistent
with the model (Fulle et al. 2019) linking the metres-thick south-
ern erosion of pristine nucleus material to the northern fallout.
Using Eqs. (2) and (3) in Fulle et al. (2019), it is possible to
estimate the pure ice and pure refractory mass ejection rates
ejected in the chunks. The water ice fraction in Hapi’s deposit
of (1.2 ±0.8)%in mass provides a refractory-to-ice mass ratio
ranging from 6 to 110 in the 4 ×107m3volume of pristine
nucleus material eroded at perihelion, corresponding to a pris-
tine ice mass fraction of (8 ±7)%in mass. The refractory-to-ice
mass ratio of the eroded pristine material can be compared with
the same ratio measured in CI-Chondrites and in the interstel-
lar medium (ISM). This value is in the range of 5%(Mogi et al.
2017) to 20%(Garenne et al. 2014) measured in CI-chondrites
and in the ISM (about 20%). The molecular abundance of water
ice in molecular clouds (Boogert et al. 2015), and likely in the
outer protoplanetary discs, H2O/H ≈10−4, and the hydrogen-to-
refractory mass ratio of approximately 100 in the ISM (Spitzer
2008) imply a refractory-to-water mass ratio ≈104/(18 ×100) ≈5
in the discs beyond the snow line. The differences we find in
terms of water abundance of the ices incorporated into the comet
67P could be caused by one of two different scenarios. The first
hypothesis is that the water abundance of the ices incorporated
into comet 67P were lower than the ISM value. This is supported
by observations indicating a ≤10−4abundance of the water sub-
limated from ices in the hot corinos of Solar-type protostars
(Ceccarelli et al. 2000;Visser et al. 2013). Another hypothe-
sis is that comet 67P lost some water in its formation. These
results imply water-trapping mechanisms that are more efficient
in possible asteroidal chondritic parents than in comets (Lorek
et al. 2016), a negligible water loss by the catastrophic collisions
fragmenting asteroids into chondrites (unless CI-chondrites after
their formation were enriched with water to values higher than
the ISM average), and a relatively uniform radial distribution of
water ice in the protoplanetary disc beyond the snow line, con-
sistent with the idea that significant radial mixing of the disc
explains the minerals found in comets (Fulle et al. 2017;Ogliore
et al. 2009).
Acknowledgements. We thank the anonymous referee for having significantly
improved the manuscript. OSIRIS was built by a consortium of the Max-Planck
Institut für Sonnensystemforschüng, in Güttingen, Germany, CISAS University
of Padova, Italy, the Laboratoire de Astrophysique de Marseille, France, the
Instituto de Astrofísica de Andalucía, CSIC, Granada, Spain, the Research and
Scientific Support Department of the European Space Agency, Noordwijk, The
Netherlands, the Instituto Nacional de Tecnica Aeroespacial, Madrid, Spain,
the Universidad Politechnica de Madrid, Spain, the Department of Physics
and Astronomy of Uppsala University, Sweden, and the Institut für Daten-
technik und Kommunikationsnetze der Technischen Universitat Braunschweig,
Germany. The support of the national funding agencies of Germany (DLR),
France (CNES), Italy (ASI), Spain (MEC), Sweden (SNSB), and the ESA
Technical Directorate is gratefully acknowledged. We thank the ESA teams at
ESAC, ESOC and ESTEC for their work in support of the Rosetta mission. We
made use of Arcgis 10.3.1 software together with the Matlab, Java, and ImageJ
software to perform our analysis. I.T. acknowledges the support from project
GINOP-2.3.2-15-2016-00003 “Cosmic effects and hazards”.
References
Acton Jr, C. H. 1996, Planet. Space Sci., 44, 65
Bertini, I., La Forgia, F., Fulle, M., et al. 2018, MNRAS, 482 2924
Blum, J., Gundlach, B., Krause, M., et al. 2017, MNRAS, 469, S755
Boogert, A. A., Gerakines, P. A., & Whittet, D. C. 2015, ARA&A, 53, 541
Burbine, T. H., McCoy, T. J., Meibom, A., Gladman, B., & Keil, K. 2002,
Asteroids III (Tucson, AZ: University of Arizona Press)
Cambianica, P., Cremonese, G., Naletto, G., et al. 2019, A&A 630, A15
Ceccarelli, C., Castets, A., Caux, E., et al. 2000, A&A, 355, 1129
De Sanctis, M., Capaccioni, F., Ciarniello, M., et al. 2015, Nature, 525,
500
El-Maarry, M. R., Thomas, N., Giacomini, L., et al. 2015, A&A 583, A26
El-Maarry, M. R., Groussin, O., Thomas, N., et al. 2017, Science, 355, 1392
Fougere, N., Altwegg, K., Berthelier, J.-J., et al. 2016, MNRAS, 462, S156
Fulle, M., Marzari, F., Della Corte, V., et al. 2016, ApJ, 821, 19
Fulle, M., Della, Corte, V., Rotundi, et al. 2017, MNRAS, 469, S45
Fulle, M., Bertini, I., Della Corte, V., et al. 2018, MNRAS, 476 2835
Fulle, M., Blum, J., Green, S. F., et al. 2019, MNRAS, 482, 3326
Garenne, A., Beck, P., Montes-Hernandez, G., et al. 2014, Geochim. Cosmochim.
Acta, 137, 93
A91, page 9 of 13
A&A 636, A91 (2020)
Groussin, O., Jorda, L., Auger, A.-T., et al. 2015, A&A, 583, A32
Gulkis, S., Allen, M., von Allmen, P., et al. 2015, Science, 347, a0709
Jorda, L., Gaskell, R., Capanna, C., et al. 2016, Icarus, 277, 257
Keller, H. U., Barbieri, C., Lamy, P., et al. 2007, Space Sci. Rev., 128,
433
Keller, H. U., Mottola, S., Davidsson, B., et al. 2015, A&A, 583, A34
Keller, H. U., Mottola, S., Hviid, S. F., et al. 2017, MNRAS, 469, S357
Lorek, S., Gundlach, B., Lacerda, P., & Blum, J. 2016, A&A, 587, A128
Marshall, D., Hartogh, P., Rezac, L., et al. 2017, A&A, 603, A87
MATLAB 2010. version 7.10.0 (R2010a). The MathWorks Inc., Natick,
Massachusetts
Migliorini, A., Piccioni, G., Capaccioni, F., et al. 2016, A&A, 589, A45
Mogi, K., Yamashita, S., Nakamura, T., et al. 2017, 80th Annual Meeting of the
Meteoritical Society, LPI Contrib., 1987, 6225
O’Brien, D. P., Izidoro, A., Jacobson, S. A., Raymond, S. N., & Rubie, D. C.
2018, Space Sci. Rev., 214, 47
Ogliore, R., Westphal, A., Gainsforth, Z., et al. 2009, Meteorit. Planet. Sci., 44,
1675
Ott, T., Drolshagen, E., Koschny, D., et al. 2017, MNRAS, 469, S276
Pajola, M., Lucchetti, A., Fulle, M., et al. 2017, MNRAS, 469, S636
Pajola, M., Lee, J.-C., Oklay, N., et al. 2019, MNRAS, 485,2139
Pätzold, M., Andert, T. P., Hahn, M., et al. 2018, MNRAS, 483,2337
Penasa, L., Massironi, M., Naletto, G., et al. 2017, MNRAS, 469, S741
Rotundi, A., Sierks, H., Della Corte, V., et al. 2015, Science, 347, aa a3905
Shi, X., Hu, X., Mottola, S., et al. 2018, Nat. Astron., 2, 562
Sierks, H., Barbieri, C., Lamy, P. L., et al. 2015, Science, 3476220
Spitzer Jr, L. 2008, Physical Processes in the Interstellar Medium (New Jersey:
John Wiley & Sons)
Thomas, N., Sierks, H., Barbieri, C., et al. 2015, Science, 347, a0440
Tosi, F., Capaccioni, F., Capria, M. T., et al. 2019, Nat. Astron., 3, 649
Visser, R., Jørgensen, J. K., Kristensen, L. E., Van Dishoeck, E. F., & Bergin,
E. A. 2013, ApJ, 769, 19
1Center of Studies and Activities for Space (CISAS) “G. Colombo”,
University of Padova, Via Venezia 15, 35131 Padova, Italy
2INAF Astronomical Observatory of Trieste, Via Tiepolo 11, 38121
Trieste, Italy
3INAF Astronomical observatory of Padova, Vicolo
dell’Osservatorio 5, 35122 Padova, Italy
e-mail: pamela.cambianica@inaf.it
4Department of Physics and Astronomy “Galileo Galilei”, University
of Padova, Via Marzolo 8, 35131 Padova, Italy
5CNR-IFN UOS Padova LUXOR, Via Trasea 7, 35131 Padova, Italy
6Department of Geosciences, University of Padova, Via Giovanni
Gradenigo 6, 35131 Padova, Italy
7Department of Physics and Astronomy “Galileo Galilei”, University
of Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy
8Physics Department, Allison Laboratory, Auburn University,
Auburn AL 36849, USA
9University Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
10 LESIA, Observatoire de Paris, PSL Research University, CNRS,
Univ. Paris Diderot, Sorbonne Paris Cité, UPMC Univ. Paris
06, Sorbonne Universités, 5 place Jules Janssen, 92195 Meudon,
France
11 Max Planck Institute for Solar System Research, Justusvon-Liebig-
Weg 3, 37077 Göttingen, Germany
12 Instituto de Astrofísica de Andalucía (CSIS), c/Glorieta de la
Astronomia s/n, 18008 Granada, Spain
13 Insitut für Geophysik und extraterrestrische Physik, Technische Uni-
versität Braunschweig, Mendelssohnstraße 3, 38106 Braunschweig,
Germany
14 Deutches Zentrum für Luft- und Raumfahrt (DLR), Institüt für
Planetenforschung, Rutherfordstraße 26, 12489 Berlin, Germany
15 Operations Department, European Space Astronomy Center/ESA,
Camino bajo del Castillo s/n, 28692 Villanueva de la Canada
(Madrid), Spain
16 CSFK Konkoly Observatory, H1121 Budapest, Konkoly Thege M. ut
15-17, Hungary
A91, page 10 of 13
P. Cambianica et al.: Time evolution of dust in the Hapi region of comet 67P/Churyumov-Gerasimenko
Appendix A: Boulder height measurements
Fig. A.1. Time evolution of the boulder height. The histogram shows the average height measurements for each boulder. As shown in the legend,
the results are divided into five time periods to better represent the trend.
Table A.1. Summary of the boulder height measurements.
# Image UTC S i e L H δH
(◦) (◦) (m) (m) (m)
1 21/08/14 16:42:56 1 80.5 55.3 50.0 8.4 0.8
22/08/14 8:42:50 1 44.1 36.2 8.3 8.6 1.9
29/08/14 20:42:53 2 83.9 47.1 86.1 9.1 0.9
29/08/14 21:42:53 2 70.5 31.7 25.7 9.1 0.8
29/08/14 23:12:53 2 72.4 34.3 28.8 9.1 0.8
30/08/14 2:42:53 2 42.4 11.5 8.3 9.1 1.5
30/08/14 3:42:53 2 35.3 10.2 6.8 9.6 1.8
10/09/24 11:54:24 3 50.9 41.7 12.1 9.8 1.1
22/09/14 21:09:48 3 40.3 56.3 8.1 9.5 2.1
19/06/16 11:09:40 5 61.5 26.5 15.1 8.2 0.7
2 22/08/14 8:42:50 1 40.7 26.8 9.0 10.5 1.9
29/08/14 21:42:53 2 70.8 32.2 32.1 11.2 0.8
29/08/14 23:12:53 2 65.9 29.0 24.6 11.1 0.9
01/09/14 16:42:53 2 36.9 26.3 8.3 11.1 1.9
10/09/14 11:54:24 3 45.5 56.3 11.9 11.7 1.8
22/09/14 21:09:48 3 45.0 63.1 11.5 11.5 2.1
10/12/14 6:29:11 4 79.0 14.6 62.3 12.1 0.7
19/06/16 11:09:40 5 59.8 27.5 18.9 11.1 0.8
3 21/08/14 19:42:54 1 46.7 19.1 6.4 6.0 1.5
28/08/14 20:42:53 2 73.8 46.3 22.4 6.5 0.7
29/08/14 20:42:53 2 70.6 33.9 18.5 6.5 0.7
29/08/14 21:42:53 2 76.0 37.1 27.9 6.9 0.7
29/08/14 23:12:53 2 74.7 37.4 23.7 6.5 0.7
30/08/14 2:42:53 2 45.7 33.5 7.2 7.0 1.6
30/08/14 3:42:53 2 30.9 15.9 4.2 7.0 2.2
31/08/14 15:42:53 2 45.1 12.1 7.4 7.4 1.5
01/09/14 16:42:53 2 41.0 20.7 6.5 7.5 1.5
10/09/14 11:54:24 3 40.6 56.1 6.0 7.0 2.0
22/09/14 21:09:48 3 37.4 58.8 5.7 7.5 2.3
Table A.1. continued.
# Image UTC S i e L H δH
(◦) (◦) (m) (m) (m)
10/12/14 6:29:11 4 77.0 14.2 33.3 7.7 0.7
19/06/16 11:09:40 5 57.1 30.1 9.7 6.3 0.8
4 21/08/14 19:42:54 1 24.4 19.6 5.9 13.0 3.6
22/08/14 8:42:50 1 51.3 33.0 16.5 13.2 1.5
28/08/14 20:42:53 2 66.7 43.4 31.8 13.7 1.1
29/08/14 20:42:53 2 77.1 38.4 61.5 14.1 0.9
29/08/14 21:42:53 2 64.1 25.4 29.0 14.1 1.0
29/08/14 23:12:53 2 60.6 23.5 24.1 13.6 1.0
31/08/14 15:42:53 2 43.4 10.3 13.3 14.1 1.7
10/09/14 11:54:24 3 47.4 51.0 15.6 14.3 1.5
10/12/14 6:29:11 4 75.5 15.6 57.4 14.8 0.7
19/06/16 11:09:40 5 60.1 28.6 23.4 13.5 0.8
5 21/08/14 19:42:54 1 43.9 25.3 10.1 10.5 1.8
22/08/14 8:42:50 1 45.7 30.7 11.0 10.8 1.7
28/08/14 20:42:53 2 68.4 45.8 28.8 11.4 1.0
29/08/14 20:42:53 2 69.5 31.3 29.7 11.1 0.8
29/08/14 21:42:53 2 67.2 28.5 26.6 11.2 0.9
29/08/14 23:12:53 2 76.4 38.4 45.6 11.0 0.8
30/08/14 2:42:53 2 44.6 21.2 11.3 11.4 1.5
31/08/14 15:42:53 2 42.6 10.8 10.8 11.8 1.7
01/09/14 16:42:53 2 43.0 33.6 11.1 11.9 1.7
10/09/14 11:54:24 3 44.1 52.8 11.5 11.9 1.7
Notes. For each boulder (#), the date of the image from which the height
is calculated, the corresponding UTC as reported in the file name (this
time not corrected for S/C drift and leap seconds), the corresponding
subset (S), the incidence angle (i), the emission angle (e), the measured
length of the shadow (L), and the measured height of the boulder (H)
with the associated average error bar (δH).
A91, page 11 of 13
A&A 636, A91 (2020)
Table A.1. continued.
# Image UTC S i e L H δH
(◦) (◦) (m) (m) (m)
10/12/14 6:29:11 3 81.1 14.3 78.6 12.4 0.8
19/06/16 11:09:40 5 57.0 30.1 17.6 11.4 0.8
6 21/08/14 16:42:56 1 65.6 49.2 62.0 28.1 1.6
21/08/14 19:42:54 1 55.2 30.3 40.0 27.8 1.7
22/08/14 8:42:50 1 49.3 37.5 32.5 28.0 2.0
29/08/14 20:42:53 2 59.5 22.4 48.8 28.7 1.3
29/08/14 21:42:53 2 68.6 30.0 73.2 28.7 1.3
29/08/14 23:12:53 2 66.5 27.3 65.8 28.7 1.3
30/08/14 2:42:53 2 48.9 11.2 32.6 28.4 1.5
30/08/14 3:42:53 2 39.4 15.5 23.4 28.4 2.0
31/08/14 15:42:53 2 49.6 4.9 33.4 28.4 1.6
01/09/14 16:42:53 2 48.5 37.7 32.8 29.0 1.8
10/09/14 11:54:24 3 58.4 41.4 48.3 29.7 1.3
22/09/14 21:09:48 3 55.4 53.7 41.3 28.5 1.6
19/06/16 11:09:40 5 62.3 26.8 52.8 27.7 1.1
7 21/08/14 19:42:54 1 49.4 26.7 18.2 15.6 1.7
29/08/14 20:42:53 2 77.1 39.4 71.7 16.4 1.0
29/08/14 21:42:53 2 69.8 30.9 43.8 16.1 1.0
29/08/14 23:12:53 2 40.0 18.6 13.5 16.1 1.8
10/09/14 11:54:24 3 44.9 45.7 16.9 17.0 1.6
22/09/14 21:09:48 3 48.1 46.5 18.5 16.6 1.4
10/12/14 6:29:11 4 68.9 22.9 44.9 17.3 0.7
19/06/16 11:09:40 5 66.5 25.1 36.6 15.9 0.8
8 29/08/2014 20:42:53 2 75.5 37.0 21.7 5.6 0.6
29/08/2014 21:42:53 2 59.9 20.9 10.3 6.0 0.9
30/08/2014 2:42:53 2 49.8 23.4 6.9 5.8 1.2
10/9/2014 11:54:24 3 49.6 40.2 7.8 6.6 1.1
22/09/2014 21:09:48 3 52.7 34.4 8.0 6.1 0.9
10/12/2014 6:29:11 4 61.0 32.7 12.3 6.8 0.6
19/06/2016 11:09:40 5 62.8 25.7 11.3 5.8 0.6
30/09/2016 3:37:09 6 86.0 62.2 83.0 5.8 0.8
9 29/08/2014 21:42:53 2 65.8 28.6 24.9 11.2 0.9
29/08/2014 23:12:53 2 72.2 32.8 35.6 11.4 0.8
10/9/2014 11:54:24 3 50.0 47.2 14.3 12.0 1.3
22/09/2014 21:09:48 3 57.6 57.3 18.7 11.9 1.3
10 29/08/2014 14:42:55 2 54.4 43.9 6.1 4.4 1.3
29/08/2014 21:42:53 2 62.9 28.6 7.7 3.9 0.8
29/08/2014 23:12:53 2 67.7 30.2 9.6 3.9 0.7
30/08/2014 2:42:53 2 53.0 24.7 5.9 4.5 1.1
30/08/2014 3:42:53 2 49.0 22.0 4.5 3.9 1.2
31/08/2014 15:42:53 2 56.6 5.6 6.5 4.3 0.9
1/9/2014 16:42:53 2 53.8 39.6 6.0 4.4 1.2
10/9/2014 11:54:24 3 60.1 45.4 8.4 4.8 0.8
22/09/2014 21:09:48 3 51.9 51.8 5.8 4.5 1.2
19/06/2016 11:09:40 5 74.6 29.3 12.0 3.3 0.4
11 21/08/2014 19:42:54 1 62.7 42.2 57.1 29.5 1.6
21/08/2014 20:42:54 1 56.6 34.6 45.3 29.8 1.7
22/08/2014 8:42:50 1 59.4 51.0 50.7 30.0 1.8
29/08/2014 14:42:55 2 58.4 34.7 49.1 30.2 1.5
29/08/2014 20:42:53 2 50.5 12.0 37.8 31.2 1.5
29/08/2014 21:42:53 2 61.2 23.2 55.6 30.6 1.4
30/08/2014 2:42:53 2 60.2 21.3 53.2 30.5 1.4
31/08/2014 15:42:53 2 59.4 18.2 50.6 30.0 1.5
1/9/2014 16:42:53 2 57.5 49.6 47.9 30.5 1.7
22/09/2014 21:09:48 3 59.2 43.5 52.1 31.0 1.3
10/12/2014 6:29:11 4 65.5 26.1 69.2 31.5 1.1
Table A.1. continued.
# Image UTC S i e L H δH
(◦) (◦) (m) (m) (m)
12 21/08/2014 19:42:54 1 66.7 47.4 40.1 17.2 1.3
21/08/2014 20:42:54 1 62.0 37.0 32.0 17.0 1.3
22/08/2014 8:42:50 1 66.0 54.9 39.1 17.4 1.4
29/08/2014 14:42:55 2 60.9 39.4 32.4 18.0 1.2
29/08/2014 23:12:53 2 62.9 26.3 34.9 17.8 1.1
30/08/2014 2:42:53 2 61.1 22.7 32.2 17.7 1.1
30/08/2014 3:42:53 2 55.3 24.2 26.1 18.1 1.3
31/08/2014 15:42:53 2 60.6 20.0 32.2 18.1 1.2
1/9/2014 16:42:53 2 59.8 50.4 31.1 18.1 1.4
22/09/2014 21:09:48 3 62.4 41.6 35.4 18.5 1.0
13 21/08/2014 16:42:56 1 71.9 54.2 52.0 17.0 1.2
21/08/2014 20:42:54 1 64.1 42.0 35.0 17.0 1.3
22/08/2014 8:42:50 1 66.7 57.8 39.0 16.8 1.4
29/08/2014 14:42:55 2 65.6 34.5 37.6 17.0 1.1
29/08/2014 20:42:53 2 35.2 13.0 12.1 17.1 2.0
29/08/2014 23:12:53 2 66.6 13.0 39.9 17.2 1.1
30/08/2014 2:42:53 2 66.4 26.7 41.3 18.1 1.0
30/08/2014 3:42:53 2 60.0 24.1 31.5 18.2 1.2
31/08/2014 15:42:53 2 67.3 25.4 43.1 18.0 1.1
1/9/2014 16:42:53 2 64.9 55.8 37.7 17.6 1.3
22/09/2014 21:09:48 3 67.1 38.1 42.9 18.1 0.9
19/06/2016 11:09:40 5 79.3 30.4 90.0 17.0 1.0
14 21/08/2014 19:42:54 1 69.8 51.9 47.5 17.5 1.3
21/08/2014 20:42:54 1 65.2 41.3 37.9 17.5 1.3
22/08/2014 8:42:50 1 76.9 68.0 74.5 17.4 1.4
28/08/2014 20:42:53 2 45.7 19.3 18.5 18.1 1.5
29/08/2014 14:42:55 2 66.6 41.8 40.8 17.6 1.1
29/08/2014 20:42:53 2 35.3 7.8 12.8 18.1 1.9
29/08/2014 21:42:53 2 42.2 15.0 16.4 18.1 1.6
29/08/2014 23:12:53 2 62.2 13.6 34.5 18.2 1.1
30/08/2014 2:42:53 2 67.4 28.2 43.8 18.2 1.0
30/08/2014 3:42:53 2 64.7 28.3 38.8 18.3 1.1
31/08/2014 15:42:53 2 69.9 26.8 50.6 18.5 1.1
1/9/2014 16:42:53 2 67.9 56.7 46.7 19.0 1.3
22/09/2014 21:09:48 3 71.2 38.7 55.1 18.7 0.9
10/12/2014 6:29:11 4 53.1 39.9 25.6 19.2 1.1
19/06/2016 15:30:03 5 69.3 16.6 47.2 17.8 0.8
30/09/2016 3:37:09 6 65.4 42.9 38.1 17.4 0.8
15 29/08/2014 14:42:55 2 54.9 34.5 31.3 22.0 1.4
29/08/2014 23:12:53 2 64.9 32.4 59.1 21.6 1.1
30/08/2014 2:42:53 2 62.0 25.7 41.4 22.1 1.2
30/08/2014 3:42:53 2 56.3 21.1 32.1 21.4 1.3
31/08/2014 15:42:53 2 65.6 19.8 47.2 21.4 1.2
1/9/2014 16:42:53 2 64.8 54.0 46.8 22.0 1.4
22/09/2014 21:09:48 3 71.8 43.6 67.7 22.3 1.0
30/09/2016 3:37:09 6 69.8 44.3 42.6 20.0 0.9
16 21/08/2014 19:42:54 1 58.4 44.0 28.3 17.4 1.5
21/08/2014 20:42:54 1 52.7 37.5 22.8 17.3 1.7
22/08/2014 8:42:50 1 71.3 65.9 51.0 17.3 1.4
29/08/2014 14:42:55 2 55.1 28.3 25.3 17.6 1.3
29/08/2014 20:42:53 2 50.4 13.2 21.8 18.0 1.3
29/08/2014 21:42:53 2 55.5 19.3 26.3 18.1 1.2
29/08/2014 23:12:53 2 53.4 14.9 23.9 17.7 1.2
30/08/2014 2:42:53 2 57.7 16.8 29.1 18.4 1.2
30/08/2014 3:42:53 2 52.7 11.5 24 18.3 1.2
31/08/2014 15:42:53 2 59.4 25.4 31.1 18.4 1.3
1/9/2014 16:42:53 2 57.7 53.1 28.8 18.2 1.6
22/09/2014 21:09:48 3 60.3 35.2 32.6 18.6 1.0
A91, page 12 of 13
P. Cambianica et al.: Time evolution of dust in the Hapi region of comet 67P/Churyumov-Gerasimenko
Table A.1. continued.
# Image UTC S i e L H δH
(◦) (◦) (m) (m) (m)
10/12/2014 6:29:11 4 68.2 24.8 47.8 19.1 0.8
19/06/2016 11:09:40 5 79.4 20.9 93.0 17.4 1.0
19/06/2016 15:30:03 5 73.4 13.1 59.2 17.6 0.8
30/09/2016 3:37:09 6 70.3 50.0 49.3 17.7 0.9
17 21/08/2014 20:42:54 1 57.1 38.8 16.2 10.5 1.4
29/08/2014 20:42:53 2 41.4 2.7 10.0 11.3 1.4
29/08/2014 21:42:53 2 47.1 8.6 11.9 11.1 1.2
30/08/2014 2:42:53 2 64.2 23.4 23.0 11.1 0.9
30/08/2014 3:42:53 2 56.2 16.4 16.8 11.2 1.1
31/08/2014 15:42:53 2 56.7 21.6 17.3 11.4 1.2
22/09/2014 21:09:48 3 64.0 40.3 24.2 11.8 0.8
10/12/2014 6:29:11 4 49.9 43.1 14.6 12.3 1.1
19/06/2016 11:09:40 5 78.0 23.1 51.0 10.8 0.7
19/06/2016 15:30:03 5 70.8 15.5 29.7 10.4 0.6
30/09/2016 3:37:09 6 62.0 40.0 19.9 10.6 0.7
18 21/08/2014 19:42:54 1 75.7 50.6 14.3 3.6 0.7
22/08/2014 8:42:50 1 67.8 55.0 13.5 5.5 1.0
29/08/2014 14:42:55 2 63.0 37.5 11.4 5.8 0.9
29/08/2014 20:42:53 2 45.8 8.2 5.3 5.2 1.2
29/08/2014 21:42:53 2 61.0 27.6 10.5 5.8 0.9
29/08/2014 23:12:53 2 72.8 35.4 13.1 4.1 0.6
30/08/2014 2:42:53 2 66.9 27.9 10.2 4.3 0.7
30/08/2014 3:42:53 2 67.7 29.5 12.5 5.1 0.7
31/08/2014 15:42:53 2 71.9 24.6 19.1 6.2 0.7
1/9/2014 16:42:53 2 68.0 54.3 12.9 5.2 0.9
22/09/2014 21:09:48 3 75.7 44.9 22.1 5.6 0.5
10/12/2014 6:29:11 4 65.3 27.8 13.3 6.2 0.5
19/06/2016 15:30:03 5 74.3 12.7 16.0 4.5 0.4
30/09/2016 3:37:09 6 68.5 50.4 11.2 4.4 0.6
19 29/08/2014 14:42:55 2 57.0 28.7 17.0 11.1 1.1
29/08/2014 23:12:53 2 53.8 14.7 14.5 10.6 1.1
30/08/2014 2:42:53 2 60.5 24.6 18.0 10.2 1.0
30/08/2014 3:42:53 2 65.0 24.1 21.8 10.2 0.9
31/08/2014 15:42:53 2 63.6 36.2 21.1 10.5 1.1
22/09/2014 21:09:48 3 67.3 30.8 26.4 11.1 0.7
10/12/2014 6:29:11 4 59.4 32.7 19.6 11.6 0.7
19/06/2016 11:09:40 5 78.9 19.3 51.0 10.0 0.6
19/06/2016 15:30:03 5 75.5 17.6 36.3 9.4 0.5
30/09/2016 3:37:09 6 70.3 40.7 27.5 9.9 0.6
20 21/08/2014 20:42:54 1 60.6 29.6 9.3 5.2 1.0
22/08/2014 8:42:50 1 66.6 48.3 12.8 5.5 1.0
29/08/2014 23:12:53 2 73.5 35.2 20.6 6.1 0.6
31/08/2014 15:42:53 2 60.5 15.4 11.5 6.5 0.9
1/9/2014 16:42:53 2 65.4 48.0 13.1 6.0 0.9
21 21/08/2014 20:42:54 1 68.1 38.7 20.2 8.1 0.9
22/08/2014 8:42:50 1 65.9 47.0 18.1 8.1 1.0
29/08/2014 21:42:53 2 54.6 16.4 12.2 8.7 1.0
1/9/2014 16:42:53 2 54.6 41.9 12.6 8.9 1.3
10/12/2014 6:29:11 4 46.2 45.8 10.0 9.6 1.2
30/09/2016 3:37:09 6 76.7 52.4 33.7 8.0 0.6
22 28/08/2014 20:42:53 2 72.9 45.7 11.4 3.5 0.6
29/08/2014 21:42:53 2 73.1 34.8 11.2 3.4 0.6
29/08/2014 23:12:53 2 74.6 36.6 12.2 3.4 0.5
30/08/2014 2:42:53 2 44.0 25.7 3.3 3.4 1.5
1/9/2014 16:42:53 2 37.1 31.6 3.0 4.0 1.9
10/9/2014 11:54:24 3 45.0 51.9 4.0 4.0 1.5
22/09/2014 21:09:48 3 51.3 57.3 5.1 4.1 1.4
A91, page 13 of 13
